You may have seen this little proof that 2=1:

a = x [true for some a's and x's]
a+a = a+x [add a to both sides]
2a = a+x [a+a = 2a]
2a-2x = a+x-2x [subtract 2x from both sides]
2(a-x) = a+x-2x [2a-2x = 2(a-x)]
2(a-x) = a-x [x-2x = -x]
2 = 1 [divide both sides by a-x]

You may doubt that 2=1. So, where is the mistake? Think about it.

You may not like the first step (a=x). But, we do this kind of thing all the time in Algebra. It's true for plenty of a's and x's. Assume that a is the number of ears on my head, and x is the number of ears on your head. In that case a=x (if a is not equal to x, forgive me for mentioning it).

Anyway, all of the steps are perfectly legal except for the last one, dividing both sides by a-x. What is a-x? Well, a=x (step 1), so a-x=0. In the last step, we divided by zero. That's not allowed. And this puzzle is a good example of why it is not allowed.

Trích đoạn: banh2005

Không tui học trong sách đâu có thấy.

Trích đoạn: banh2005

A=B=1
=> A+1=B+1
=> A-1=B-1
=> A bình phương -1=B bình phương -1
=> (A+1).(A-1)=B(B-1)

=> (A+1).(A-1)= A(A-1)
__________________________
(A-1)

=> 2=1

_______ : phép chia

Đáng lẻ post hình lên nhưng tới 1MB nên không được, hơi khó hiểu 1 tí nhé.

Trích đoạn: An_Nam2001


Như vậy thì ai chứng minh được

1 = -1

Trích đoạn: nobita1984

Làm sao có căn bậc 2 của dấu âm đc